Statistics Seminar: John Robinson -- Relative Error of the Bootstrap for Serial Correlation

John Robinson School of Mathematics and Statistics University of Sydney 

Location: Carslaw 273 

Time: 2pm Friday, Jun 8, 2012 

Title: Relative Error of the Bootstrap for Serial Correlation 

Abstract: Consider the first serial correlation coefficient under an AR(1) model where
errors are not assumed to be Gaussian.  In this case it is in general necessary to
consider bootstrap approximations for tests based on the statistic when the distribution
of observations is unknown.  We obtain saddle-point approximations for tail
probabilities of the statistic and its bootstrap version and use these to show that the
bootstrap tail probabilities approximate the true values with given relative errors,
thus extending the classical results of Daniels [Biometrika 43 (1956) 169-185] for the
Gaussian case.  The methods require conditioning on the set of odd numbered
observations.